It is unlikely you have an isolated problem with the posterior talofibular ligament. This ligament can be injured in severe ankle sprains and result in instability, but is rarely an isolated problem without a history of trauma. With an ankle sprain, is more common to tear the anterior talofibular ligament or the calcaneofibular ligament. Previous ankle sprains and inherited hypermobility can result in ankle instability.
The ankle ligaments are shown in the image below.
The peroneal tendons course right over the ankle ligaments and the area you have described the feeling of a slipping or popping sensation.
The peroneal tendons are shown in the image below.
Normally, there is a structure which holds these tendons in place behind the fibula. If there is any damage to this structure, these tendons can sublux. This means that they can "slip in front of the bone." This generally happens when walking, and most commonly during push off.
The "slipping" sensation and sometimes pain occur as the heel rises during push off as seen in the image below.
Another possibility is a problem with the an accessory bone called the os trigonum. When the foot is fully flexed (plantar flexed) this bone can become impinged causing sharp pain in the back of the ankle. When up on the toes the pain can be sharp and result in instability (ankle sprains) and this is called posterior impingement syndrome. This is most commonly seen in ballerinas.
The os trigonum is circled in the image below.
There are other potential problems that can cause the types of symptoms you are experiencing. Unfortunately, all of them involve a trip to the doctor's office and a full evaluation of the foot and ankle.